The Constitutional Court will decide whether the European Stability Mechanism (ESM) bailout fund and the European fiscal treaty are legal.
It is feared a negative decision could spark fresh turmoil in the markets.
Analysts expect the court will decide the schemes are legal and can continue – but only under certain conditions.
The court has recently allowed steps towards greater European integration, but has insisted the German parliament be given a greater say over decisions.
Critics argue that the ESM commits Germany to potentially unlimited funding of debt-ridden southern eurozone countries.
Some 37,000 people have signed a petition to the court asking it to block the ESM, and make it subject to a referendum.
Since Germany is due to contribute 27% to the 500 billion-euro rescue fund, it cannot proceed without German ratification.
In addition to its ESM verdict, the Constitutional Court is also due to rule on a new fiscal treaty aimed at forcing eurozone governments to adhere to strict budget discipline.
This is one of the most important cases faced by the court in post-war German history.
It has caused intense debate, with politicians and lawyers from across the political spectrum joining the case against the government – from the left party, Die Linke, to dissidents from within the government party.
If the judges take a hard line against the government and in favor of the plaintiffs, then the elaborate and laborious efforts to keep the euro together will be dealt a severe blow, perhaps a fatal one.
A likely outcome is that the judges will say the treaties are within the constitution – but then put a string of caveats in place, which might constrain, for instance, how the bailout fund could be expanded in the future.
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